Abstract Succinct Non-interactive Arguments of Knowledge (SNARKs) allow an untrusted
prover to establish that it correctly ran some “witness-checking procedure” on a witness. A …

This paper introduces customizable constraint system (CCS), a generalization of R1CS that
can simultaneously capture R1CS, Plonkish, and AIR without overheads. Unlike existing …

We introduce and study a simple kind of proof system called line-point zero knowledge
(LPZK). In an LPZK proof, the prover encodes the witness as an affine line $\mathbf …

Recently there has been much academic and industrial interest in practical implementations
of zero knowledge proofs. These techniques allow a party to prove to another party that a …

We present a generalized inner product argument and demonstrate its applications to
pairing-based languages. We apply our generalized argument to prove that an inner pairing …

The disruptive blockchain technology is expected to have broad applications in many areas
due to its advantages of transparency, fault tolerance, and decentralization, but the open …

Advanced cryptographic protocols such as Zero-knowledge (ZK) proofs of knowledge,
widely used in cryptocurrency applications such as Zcash, Monero, Filecoin, Tezos, Topos …

This paper introduces SuperNova, a new recursive proof system for incrementally producing
succinct proofs of correct execution of programs on a stateful machine with a particular …

A zero-knowledge (ZK) proof guarantees that the result of a computation is correct while
keeping part of the computation details private. Some ZK proofs are tiny and can be verified …

This paper introduces Brakedown, 1 the first built system that provides linear-time SNARKs
for NP, meaning the prover incurs O (N) finite field operations to prove the satisfiability of an …